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L. van der Linden
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Master thesis
(2024)
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L. van der Linden, Joris Bentvelsen, S. Jain, M.B. van Gijzen, A.B.T. Barbaro
This thesis explores the improvement of computational efficiency in simulating two-dimensional conveyor belt systems by applying model order reduction (MOR) techniques. Conveyor belts, crucial for material handling in various industries, are traditionally modeled using finite element methods (FEM), which can be computationally demanding, particularly for long-term simulations with a high number of grid elements. To address this, MOR techniques aim to reduce high-dimensional models into lowerdimensional models.
The study investigates three MOR approaches—modal decomposition, Proper Orthogonal Decomposition (POD), and Dynamic Mode Decomposition (DMD)—to apply on existing software built by VORtech that simulates two-dimensional conveyor belt systems. When considering MOR to reduce the two-dimensional system, challenges arise related to nonlinearities, differential algebraic equations (DAEs), and complex modeling steps. Among the methods tested, DMD proved to be the most effective, offering significant reductions in computational time while maintaining accuracy. POD also demonstrated accuracy but had less impact on speed due to the time-consuming complex modeling steps in the simulation software. These complex modeling steps are not investigated in detail in this thesis and therefore not reducible with the intrusive POD. Because of the non-intrusive nature of DMD, this method was able to incorporate these extra processes in the reduced order model.
The study concludes with recommendations for future research, emphasizing the need for optimization of the code segments that handle the complex modeling steps. In addition, conventional modeling approaches as alternatives to the complex interpolation step could be explored, to enhance the applicability of MOR. Furthermore, DMD with control or parametric DMD could be explored to obtain a reduced order model by interpreting misalignments of rollers as controls or parameters. Finally, a method is proposed to make modal decomposition useful for models, where the solutions depend highly on the external forces. Although this method is not applied to the model considered in this thesis, it would be interesting to explore this modified modal decomposition method on other models that are significantly influenced by the external forces. ...
The study investigates three MOR approaches—modal decomposition, Proper Orthogonal Decomposition (POD), and Dynamic Mode Decomposition (DMD)—to apply on existing software built by VORtech that simulates two-dimensional conveyor belt systems. When considering MOR to reduce the two-dimensional system, challenges arise related to nonlinearities, differential algebraic equations (DAEs), and complex modeling steps. Among the methods tested, DMD proved to be the most effective, offering significant reductions in computational time while maintaining accuracy. POD also demonstrated accuracy but had less impact on speed due to the time-consuming complex modeling steps in the simulation software. These complex modeling steps are not investigated in detail in this thesis and therefore not reducible with the intrusive POD. Because of the non-intrusive nature of DMD, this method was able to incorporate these extra processes in the reduced order model.
The study concludes with recommendations for future research, emphasizing the need for optimization of the code segments that handle the complex modeling steps. In addition, conventional modeling approaches as alternatives to the complex interpolation step could be explored, to enhance the applicability of MOR. Furthermore, DMD with control or parametric DMD could be explored to obtain a reduced order model by interpreting misalignments of rollers as controls or parameters. Finally, a method is proposed to make modal decomposition useful for models, where the solutions depend highly on the external forces. Although this method is not applied to the model considered in this thesis, it would be interesting to explore this modified modal decomposition method on other models that are significantly influenced by the external forces. ...
This thesis explores the improvement of computational efficiency in simulating two-dimensional conveyor belt systems by applying model order reduction (MOR) techniques. Conveyor belts, crucial for material handling in various industries, are traditionally modeled using finite element methods (FEM), which can be computationally demanding, particularly for long-term simulations with a high number of grid elements. To address this, MOR techniques aim to reduce high-dimensional models into lowerdimensional models.
The study investigates three MOR approaches—modal decomposition, Proper Orthogonal Decomposition (POD), and Dynamic Mode Decomposition (DMD)—to apply on existing software built by VORtech that simulates two-dimensional conveyor belt systems. When considering MOR to reduce the two-dimensional system, challenges arise related to nonlinearities, differential algebraic equations (DAEs), and complex modeling steps. Among the methods tested, DMD proved to be the most effective, offering significant reductions in computational time while maintaining accuracy. POD also demonstrated accuracy but had less impact on speed due to the time-consuming complex modeling steps in the simulation software. These complex modeling steps are not investigated in detail in this thesis and therefore not reducible with the intrusive POD. Because of the non-intrusive nature of DMD, this method was able to incorporate these extra processes in the reduced order model.
The study concludes with recommendations for future research, emphasizing the need for optimization of the code segments that handle the complex modeling steps. In addition, conventional modeling approaches as alternatives to the complex interpolation step could be explored, to enhance the applicability of MOR. Furthermore, DMD with control or parametric DMD could be explored to obtain a reduced order model by interpreting misalignments of rollers as controls or parameters. Finally, a method is proposed to make modal decomposition useful for models, where the solutions depend highly on the external forces. Although this method is not applied to the model considered in this thesis, it would be interesting to explore this modified modal decomposition method on other models that are significantly influenced by the external forces.
The study investigates three MOR approaches—modal decomposition, Proper Orthogonal Decomposition (POD), and Dynamic Mode Decomposition (DMD)—to apply on existing software built by VORtech that simulates two-dimensional conveyor belt systems. When considering MOR to reduce the two-dimensional system, challenges arise related to nonlinearities, differential algebraic equations (DAEs), and complex modeling steps. Among the methods tested, DMD proved to be the most effective, offering significant reductions in computational time while maintaining accuracy. POD also demonstrated accuracy but had less impact on speed due to the time-consuming complex modeling steps in the simulation software. These complex modeling steps are not investigated in detail in this thesis and therefore not reducible with the intrusive POD. Because of the non-intrusive nature of DMD, this method was able to incorporate these extra processes in the reduced order model.
The study concludes with recommendations for future research, emphasizing the need for optimization of the code segments that handle the complex modeling steps. In addition, conventional modeling approaches as alternatives to the complex interpolation step could be explored, to enhance the applicability of MOR. Furthermore, DMD with control or parametric DMD could be explored to obtain a reduced order model by interpreting misalignments of rollers as controls or parameters. Finally, a method is proposed to make modal decomposition useful for models, where the solutions depend highly on the external forces. Although this method is not applied to the model considered in this thesis, it would be interesting to explore this modified modal decomposition method on other models that are significantly influenced by the external forces.
In this work, the parareal algorithm is analysed and executed on the model for combustion of methane. The parareal algorithm is designed to generate an approximation to an initial value problem faster than a serial numerical time-integration method by using two propagators, the coarse propagator and the fine propagator. With the use of two different propagators, some computations can be carried out in parallel, which leads to a faster method. In this research, the parareal algorithm is executed on the two-step mechanism for combustion of methane. The temperature rise due to the combustion is assumed to be zero. The model is implemented in Python and with the use of the librarymultiprocessing, computations are executed in parallel. Different time-integration methods are implemented that can be used in the coarse and fine propagator. In this research, we will focus on the case that the both propagators use the same time-integration method. One can distinguish the propagators by using a different time-step for a chosen time-integration method. With the use of the absolute error the accuracy can be examined. Because the analytic solution to the problem for combustion of methane is unknown, a time-integration method, from which we know that it gives a small absolute error, is used as representation of the analytic solution. The parareal algorithm executed on the model for combustion of methane gives an accurate result for the right choice of propagators. However, for this choice of propagators, the parareal algorithm does not result in a significant speedup compared to the fine propagator in serial, assuming that we have enough processors available. This is because the running time of the propagators do not differ much. To generate a better speedup, two different time-integration methods can be considered for the propagators. Moreover, the model for combustion of methane can be divided into more than two partial reaction and then themulti-level parallelization [1] can be examined.
...
In this work, the parareal algorithm is analysed and executed on the model for combustion of methane. The parareal algorithm is designed to generate an approximation to an initial value problem faster than a serial numerical time-integration method by using two propagators, the coarse propagator and the fine propagator. With the use of two different propagators, some computations can be carried out in parallel, which leads to a faster method. In this research, the parareal algorithm is executed on the two-step mechanism for combustion of methane. The temperature rise due to the combustion is assumed to be zero. The model is implemented in Python and with the use of the librarymultiprocessing, computations are executed in parallel. Different time-integration methods are implemented that can be used in the coarse and fine propagator. In this research, we will focus on the case that the both propagators use the same time-integration method. One can distinguish the propagators by using a different time-step for a chosen time-integration method. With the use of the absolute error the accuracy can be examined. Because the analytic solution to the problem for combustion of methane is unknown, a time-integration method, from which we know that it gives a small absolute error, is used as representation of the analytic solution. The parareal algorithm executed on the model for combustion of methane gives an accurate result for the right choice of propagators. However, for this choice of propagators, the parareal algorithm does not result in a significant speedup compared to the fine propagator in serial, assuming that we have enough processors available. This is because the running time of the propagators do not differ much. To generate a better speedup, two different time-integration methods can be considered for the propagators. Moreover, the model for combustion of methane can be divided into more than two partial reaction and then themulti-level parallelization [1] can be examined.